What is a rational number with a denominator of 7 that is between square root of 7 and square root of 8. Write your answer as an improper fraction
To find a rational number with a denominator of 7 that lies between √7 and √8, we can convert both square roots to fractions with a denominator of 7, and then average those fractions.
√7 ≈ 7/7 = 49/7
√8 ≈ 8/7
Taking the average of 49/7 and 8/7 gives us:
(49/7 + 8/7) / 2 = 57/14
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 57/14 (written as an improper fraction).
it says with a denominator of 7
Apologies for the misunderstanding. To find a rational number with a denominator of 7 that lies between √7 and √8, we can multiply both square roots by 7 to obtain fractions with a denominator of 7.
√7 * 7 = 7√7 ≈ 7(2.65) = 18.55 ≈ 19
√8 * 7 = 7√8 ≈ 7(2.83) = 19.81 ≈ 20
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 19/7 (written as an improper fraction).
To find a rational number with a denominator of 7 between the square root of 7 and the square root of 8, we need to check which rational numbers with a denominator of 7 lie between these two square roots.
First, let's calculate the decimal equivalents of the square roots of 7 and 8.
The square root of 7 is approximately 2.645751311.
The square root of 8 is approximately 2.828427125.
Now, let's find the rational numbers with a denominator of 7 that lie between these two decimal values.
The fraction 3/7 is approximately 0.428571429.
The fraction 4/7 is approximately 0.571428571.
Comparing these decimal values to the decimal equivalents of the square roots, we can see that 3/7 lies between the square root of 7 and the square root of 8.
Therefore, the rational number is 3/7.
To find a rational number with a denominator of 7 between √7 and √8, we need to examine the decimal values of √7 and √8.
First, calculate the decimal approximations of both square roots:
√7 ≈ 2.65
√8 ≈ 2.83
Since we want a rational number with a denominator of 7, we can consider multiples of 7 as possible numerators.
Now we need to select an appropriate numerator that will make the fraction fall between 2.65 and 2.83. To do this, we can compare each multiple of 7 when written as a fraction with a denominator of 7.
For instance, let's consider the multiple of 7 as the numerator:
Numerator = 7 x 4 = 28
We can write the fraction as 28/7, which simplifies to
28/7 = 4
This fraction is equal to 4 as an improper fraction, and it lies between √7 and √8. Therefore, the rational number we found is 4/1, which can be written as an improper fraction as 4.